Jack Kinseth | Searcharxiv

arXiv2022

Conditions for matchability in groups and field extensions

The origins of the notion of matchings in groups spawn from a linear algebra problem proposed by E. K. Wakeford [24] which was tackled in 1996 [10]. In this paper, we first discuss unmatchable subsets in abelian groups. Then we formulate and prove linear analogues of results concerning matchings, along with a conjecture that, if true, would extend the primitive subspace theorem. We discuss the dimension $m$-intersection property for vector spaces and its connection to matching subspaces in a field extension, and we prove the linear version of an intersection property result of certain subsets of a given set.

math.CO↗

arXiv2020

A meta-analysis of Boolean network models reveals design principles of gene regulatory networks

Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean networks, which are intuitive, simple to describe, and can yield qualitative results even when data is sparse. We assembled the largest repository of expert-curated Boolean GRN models. A meta-analysis of this diverse set of models reveals several design principles. GRNs exhibit more canalization, redundancy and stable dynamics than expected. Moreover, they are enriched for certain recurring network motifs. This raises the important question why evolution favors these design mechanisms.

q-bio.MN↗